For example, f(x,y)= 3x+ 2y and are functions of two variables. f(1, 2)= 3(1)+ 2(2)= 3+ 4= 7 and . Quite often you can think of z= f(x,y) as defining a surface. At each value of x and y, z is the height of the surface above (or below is f(x,y) is negative) the xy-plane.
For these examples, f(x,y)= 3x+ 2y is the equation of a plane and is a "paraboloid".
(f(x,y), in general, doesn't have anything to do with Number Theory.)
Thanks, I thought it had something to do with binary relations.
I've also noticed that graphing such functions is quite difficult. I saw that you said that " is a "paraboloid"." Can I guess the shape of a function by looking at the degree of the variables of the function i.e. would g(x, y) = x^3 + y^3 be some sort of hour-glass shape?
(Some background on these seemingly simple questions: I'm a first year physics student, I walked into the wrong lecture room and was too ashamed to get up in the middle of a class so I stayed and learned something about PDE's. Not much, but something... Partial derivatives actually make a lot of sense in the context of geometry- I would always get really pissed whenever I would encounter a related rates question in highschool calc involving geometry where a height variable would be held constant- now with partial differentiation I don't have to answer one part of the question... anyway, thanks)
When I was in graduate school, this really, really, young guy came into the class room. I guessed he was an undergraduate, probably a freshman, who had come into the wrong room and wondered if he would have the courage to leave when he discovered his error. It turned out he was the professor!
I remember I was having a calculus 3 course along with a physics course involving the heat equation... I'm almost sure it's common.